On star-Moments of the compression of the free unitary Brownian motion by a free projection

Autor:	Demni, Nizar, Hamdi, Tarek
Rok vydání:	2020
Předmět:	Mathematics - Operator Algebras Mathematics - Classical Analysis and ODEs Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	In this paper, we derive explicit expressions for the moments and for the mixed moments of the compression of a free unitary Brownian motion by a free projection. While the moments of this non-normal operator are readily derived using analytical or combinatorial methods, we only succeeded to derive its mixed ones after solving a non-linear partial differential equation for their two-variables generating function. Nonetheless, the combinatorics of non crossing partitions lead to another expression of the lowest-order mixed moment. We shall also give some interest in odd alternating moments. In particular, we derive a linear partial differential equation for their generating function and discuss the combinatorial approach to these moments when the rank of the projection equals $1/2$. Comment: Extended version with further results
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2001.06876 Zobrazit plný text záznamu View this record from Arxiv